This invention is in the field of seismic prospecting for oil and gas reservoirs, and is more specifically directed to inversion analysis of seismic surveys.
As is well known in the art of seismic prospecting for hydrocarbon (i.e., oil and gas) reservoirs in the earth, inversion is an attractive technique for automating the interpretation of seismic results. In general, inversion refers to the analytical approach in which time-domain signals corresponding to the reflection of acoustic energy from reflective interfaces between subsurface strata in the earth are converted into one or more traces representative of physical attributes of the strata. In contrast, seismic reflection surveys provide only an indication of the contrast of layer properties at a reflective interface between the layers.
In practice, conventional seismic inversion typically begins by creating a model of the surveyed region based upon an extraction of the geological properties of the detected subsurface strata. These geological properties are typically measured by way of well logs and the like, at calibration points in the survey. This model is then used to generate synthetic seismograms, which are compared against actual seismic reflection traces at the calibration points; iterative techniques are then applied to match the model to the actual reflection traces, and to then extract a representation of the input wavelet. The extracted input wavelet is then used to derive a filter operator that can be applied to the overall seismic data, by frequency-domain division (or equivalent time-domain deconvolution) or by other techniques such as sparse spike inversion, to effect the inversion of the reflection traces into a series of reflection coefficients. These reflection coefficients are converted into velocity and density values for the surveyed layers, completing the inversion.
Impedance-based inversion is a known inversion technique in modem seismic prospecting. In this conventional example of impedance inversion, the initial model is based upon the combination of a sonic (velocity) log with a density log, at one or more drilling locations. Through inversion based upon this model, the seismic reflectivity section is converted into a section that represents the acoustic impedance of the various represented strata to the imparted seismic energy, as a function of position and depth in the region. Because acoustic impedance corresponds to the product of the density and acoustic velocity of the medium, the acoustic impedance can indicate actual physical properties of the rock, such as porosity and the composition of material in the rock pores (i.e., pore fill). Accordingly, impedance inversion sections are potentially much more informative to the geologist than are reflectivity sections, which simply indicate the location of reflective subsurface interfaces and the nature of contrasts in rock properties thereat. Indeed, reflectivity sections are unable to distinguish among possible physical causes of the reflections; for example, a reflection due to a change in the rock properties of the reservoir interval may appear quite similar to a reflection due to a change in the properties of an overlying seal. In addition, impedance inversion techniques can be used to remove the input wavelet from the resulting sections, improving the resolution with which the petrophysically interesting information can be retrieved from the seismic data. Impedance inversion thus eliminates some of the necessity for, and inaccuracy in, human interpretation of the seismic survey.
It is well known in the art, however, that impedance inversion from seismic reflectivity traces alone is band-limited, because the reflectivity data is itself band-limited. However, information regarding porosity and pore fill also contains "low-frequency" information, and thus cannot be directly extracted from impedance inversion of conventional reflectivity data. As a result, conventional impedance inversion analysis typically imports low frequency information from a model based on well log information and measured seismic velocities. An example of impedance inversion utilizing model information to provide the low frequency data is described in U.S. Pat. No. 4,964,096.
Several geophysical software packages for performing impedance inversion are known in the art. Examples of such products include the JASON GEOSCIENCE WORKBENCH system available from Jason Geosystems, the STRATA package available from Hampson-Russell, and the ISIS package available from Odegaard A/S. These conventional packages require a reflectivity section, background seismic velocities, and well impedance measurements. According to these known inversion techniques, the product of the well log density and velocity is used to derive the impedance measurements for each layer in the model, for calibration with zero offset seismic data.
FIG. 1 illustrates a conventional example of impedance inversion, for example as performed according to the JASON GEOSCIENCE WORKBENCH system from Jason Geosystems. As illustrated in FIG. 1, density and sonic (velocity) well logs are obtained, and applied to process 10 in which the logs are edited and tied to zero-offset (i.e., near-offset traces, stacked to zero-offset) seismic data and to previously interpreted horizons. In process 12, estimation of the input wavelet to the seismic data is performed, in the conventional manner, using the edited and tied well logs and the zero-offset seismic data at the well locations. The estimated input wavelet is then applied, as a filter, to the seismic data over the survey region, in inversion process 14; inversion is carried out, as noted above, according to one of several inversion techniques such as constrained sparse spike inversion (CSSI), stochastic inversion, and the like.
Because the seismic reflection data are band-limited, however, low frequency information regarding density and velocity is not determined in the inversion of process 14. Accordingly, in this conventional approach, process 16 generates an earth model of density and velocity using previously interpreted horizons in the survey region of interest. This earth model corresponds to low frequency variations of density and velocity, and is merged with the inversion from process 14 in process 18, to produce a density and velocity model of the earth over both low and high frequencies. This model is then analyzed in process 20, to determine such rock parameters as porosity.
However, Amplitude-versus-Offset (AVO) surveys have shown that some important hydrocarbon reservoirs exhibit relatively little reflectivity at zero offset, while exhibiting significant reflectivity at larger offsets. As with other regions of the earth that potentially contain oil and gas reservoirs, it would of course be useful to utilize impedance inversion techniques to identify the rock properties that directly relate to the presence of oil and gas, such properties including porosity and pore fill. While it is possible to construct seismic sections for a particular (relatively small) range of offset (or angle of incidence, or ray parameter), heretofore there has been no adequate mathematical definition of elastic impedance that may be used in extrapolating the limited-offset range sections over a wider range.
Consider that a desired elastic impedance expression, for a rock layer k, should be a function of its density .rho..sub.k, its compressional velocity .alpha..sub.k, its shear velocity .beta..sub.k, and the angle of incidence i, or: EQU EI.sub.k =.function.(.rho..sub.k, .alpha..sub.k, .beta..sub.k, i)
As is well known in the art, the reflectivity r(i) at an interface between two layers, as a function of angle, is the ratio of the difference of elastic impedance of the two layers to the sum of the impedances: ##EQU1## This relationship between the reflectivity and the elastic impedance of the layers could provide a link between the reflection traces and the rock properties. However, the absence of a known mathematical definition of the actual elastic impedance function has prohibited this type of analysis.
One possible approach toward an offset-dependent impedance inversion would be to use the zero offset acoustic impedance to calibrate the inversion. As noted above, however, some important reservoirs have low reflectivity at zero offset but high reflectivity at far offset. As a result, the use of zero offset impedance values in these surveys necessarily lacks the essential element necessary for accurate calibration, namely the significant far-offset reflectivity. Impedance inversion under these conditions will thus result in a poor tie to the seismic section, an incorrect extracted wavelet, poor resolution, and the inability to determine the Poisson's ratio for the reservoir.
Another possible approach toward an offset-dependent impedance inversion would be to use approximations of elastic impedance as derived from density logs and measurements or estimates of compressional and shear velocities for the various layers in the region. As noted above, no exact definition of elastic impedance as a function of the rock properties exists. However, approximations of elastic impedance over limited angle ranges near zero offset are known. For example, Connolly, "Calibration and Inversion of Non-Zero Offset Seismic", Expanded Abstracts of 1998 Annual Meeting (SEG, 1998), pp. 182-184, describes one such approximation as follows: ##EQU2## where K is the average of the ratio ##EQU3## across the interface of interest. This approximation is derived by integration of the approximation of the Zoeppritz equation as given in Aki and Richards, Quantitative seismology: Theory and Methods, (W. H. Freeman & Co., 1980), p.153. It has been observed, in connection with the present invention, that this approximation of elastic impedance depends upon average properties across an interface and also upon reference values for density, compressional velocity, and shear velocity. These dependencies render the application of this approximation very difficult when applied to multi-layer sequences of interfaces, such as are typically represented by well logs. Use of this approximation without the averaged values (in the ratio K) returns an unstable elastic impedance value, and results in inaccurate reflectivity values. Similar alternative approximations for elastic impedance have also been constructed from the inversion of reflectivities calculated from the Zoeppritz equations, but these approximations have no direct connection to rock properties, limiting their use in interpretation of the survey. In addition, the absolute magnitude of the impedance in these approximations is an integration constant, with no physical meaning.